Finite Group Databasebeta

← C151×#24890 #50329815

Subgroups — C151×#24890 #50329815

Order 38656.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C151C211yesmaximal, characteristic, complemented
2C2×#418×C151C211yesmaximal, characteristic, complemented
3#2408×C151C211yesmaximal, characteristic
4#2354×C151C211yesmaximal, characteristic, complemented
5#2093×C151C211yesmaximal, characteristic, complemented
6#2071×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1926×C151C211yesmaximal, characteristic, complemented
10#1926×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1870×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1809×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C2×#121×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×#120×C151—21no—
21C2×C4×D4×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic, complemented
24#482×C151—24no—
25C2×#107×C151C2211yescharacteristic, complemented
26C2×#107×C151C2211yescharacteristic, complemented
27C2×#106×C151C2211yescharacteristic, complemented
28C2×#106×C151C2211yescharacteristic, complemented
29#418×C151—24no—
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic, complemented
40C2×C22⋊C8×C151C2211yescharacteristic, complemented
41#394×C151—21no—
42#392×C151—21no—
43#390×C151—21no—
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic
46#388×C151—21no—
47#388×C151—21no—
48#384×C151C2211yescharacteristic, complemented
49#380×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic, complemented
52#379×C151—21no—
53C4×C4⋊C4×C151—21no—
54C4×C4⋊C4×C151C2211yescharacteristic, complemented
55#340×C151C2211yescharacteristic, complemented
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—22no—
69C22×D4×C151—41no—
70C22×D4×C151—41no—
71C22×D4×C151D411yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C22×D4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83#121×C151—22no—
84#121×C151—22no—
85#121×C151—41no—
86#121×C151—41no—
87#120×C151—44no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90#117×C151—22no—
91#117×C151—22no—
92#117×C151—41no—
93#117×C151—41no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151D411yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151D411yescharacteristic
115C2×C22⋊C4×C151D411yescharacteristic
116C2×C42×C151—21no—
117C2×C42×C151—21no—
118C2×C42×C151—21no—
119C2×C42×C151C2311yescharacteristic
120#107×C151—22no—
121#107×C151—41no—
122#106×C151—22no—
123#106×C151—41no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—41no—
130#102×C151—41no—
131#102×C151D414yescomplemented
132C22⋊C8×C151—22no—
133C22⋊C8×C151—22no—
134C22⋊C8×C151—41no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139C24×C151—21no—
140C24×C151—21no—
141C24×C151—42no—
142C24×C151—42no—
143C24×C151—42no—
144C24×C151—42no—
145C24×C151—42no—
146C24×C151—81no—
147C24×C151—81no—
148C24×C151C2×D411yescharacteristic
149C24×C151C2×D411yescharacteristic
150C2×D4×C151—28no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—44no—
164C2×D4×C151—44no—
165C2×D4×C151—41no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—44no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—42no—
174C2×D4×C151—81no—
175C2×D4×C151—81no—
176C2×D4×C151C2×D412yes—
177C2×D4×C151#4112yes—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151C2×D411yescharacteristic
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151#4112yes—
199C22×C4×C151#4112yes—
200C22×C4×C151C2411yescharacteristic
201M16×C151—44no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151C2×D412yes—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—42no—
227C4⋊C4×C151—81no—
228C4⋊C4×C151C2×D412yes—
229C22⋊C4×C151—22no—
230C22⋊C4×C151—22no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—42no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—81no—
239C22⋊C4×C151—81no—
240C22⋊C4×C151—81no—
241C22⋊C4×C151—81no—
242C42×C151—21no—
243C42×C151—21no—
244C42×C151—42no—
245C42×C151—42no—
246C42×C151—42no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—22no—
255C23×C151—21no—
256C23×C151—22no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—48no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—84no—
276C23×C151—84no—
277C23×C151—84no—
278C23×C151—84no—
279C23×C151—84no—
280C23×C151—84no—
281C23×C151#12312yes—
282C23×C151C22×D411yescharacteristic
283D4×C151—22no—
284D4×C151—22no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—44no—
288D4×C151—48no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—84no—
294D4×C151—84no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—22no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—22no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151#12312yes—
332C2×C4×C151AGL(1,ℤ/8)12yes—
333C2×C4×C151C22×D411yescharacteristic
334C2×C4×C151C2×#4111yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151C2×#4111yescharacteristic
337C2×C4×C151H(5,𝔽2)11yescharacteristic
338C2×C4×C151H(5,𝔽2)11yescharacteristic
339C8×C151—22no—
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C22×C151—22no—
344C22×C151—22no—
345C22×C151—22no—
346C22×C151—41no—
347C22×C151—41no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—41no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—42no—
359C22×C151—41no—
360C22×C151—42no—
361C22×C151—41no—
362C22×C151—42no—
363C22×C151—816no—
364C22×C151—81no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151—81no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151C2×#12311yescharacteristic
373C22×C151D4211yescharacteristic
374C22×C151#54611yescharacteristic
375C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C151#57511yescharacteristic
377C22×C151#57611yescharacteristic
378C22×C151#57711yescharacteristic
379C4×C151—22no—
380C4×C151—22no—
381C4×C151—41no—
382C4×C151—41no—
383C4×C151—42no—
384C4×C151—81no—
385C4×C151—81no—
386C4×C151—81no—
387C4×C151—81no—
388C4×C151—81no—
389C4×C151#52511yescharacteristic
390C4×C151#53811yescharacteristic
391C4×C151#54611yescharacteristic
392C4×C151#55111yescharacteristic
393C2×C151—42no—
394C2×C151—81no—
395C2×C151—82no—
396C2×C151—82no—
397C2×C151#241811yescharacteristic
398C2×C151#309411yescharacteristic
399C2×C151#309611yescharacteristic
400C2×C151#326711yescharacteristic
401C2×C151#327411yescharacteristic
402C2×C151#331911yescharacteristic
403C2×C151#332411yescharacteristic
404#24890C15111yesmaximal, characteristic, direct product factor, Sylow
405C151#2489011yescharacteristic, direct product factor, Sylow
406C2×#482C2×C15111yescharacteristic, complemented
407C2×#418C2×C15111yescharacteristic, complemented
408#2408C2×C15111yescharacteristic
409#2354C2×C15111yescharacteristic, complemented
410#2093C2×C15111yescharacteristic, complemented
411#2071C2×C15111yescharacteristic, complemented
412#2034C2×C15111yescharacteristic, complemented
413#2033C2×C15111yescharacteristic, complemented
414#1926C2×C15111yescharacteristic, complemented
415#1926C2×C15111yescharacteristic, complemented
416#1875C2×C15111yescharacteristic, complemented
417#1870C2×C15111yescharacteristic, complemented
418#1854C2×C15111yescharacteristic, complemented
419#1809C2×C15111yescharacteristic, complemented
420#1786C2×C15111yescharacteristic, complemented
421C23×D4C22×C15111yescharacteristic
422C22×M16C22×C15111yescharacteristic
423C2×#121C22×C15111yescharacteristic
424C2×#121C22×C15111yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C15111yescharacteristic
427C2×#117C22×C15111yescharacteristic
428C2×#117C22×C15111yescharacteristic, complemented
429#482—24no—
430C2×#107C22×C15111yescharacteristic, complemented
431C2×#107C22×C15111yescharacteristic, complemented
432C2×#106C22×C15111yescharacteristic, complemented
433C2×#106C22×C15111yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×#102C22×C15111yescharacteristic
438C2×#102C22×C15111yescharacteristic
439C2×#102C22×C15111yescharacteristic
440C2×#102C22×C15111yescharacteristic
441C2×#102C22×C15111yescharacteristic
442C2×#102C22×C15111yescharacteristic
443C2×C22⋊C8C22×C15111yescharacteristic
444C2×C22⋊C8C22×C15111yescharacteristic, complemented
445C2×C22⋊C8C22×C15111yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390—21no—
449#390C22×C15111yescharacteristic
450#390C22×C15111yescharacteristic
451#388—21no—
452#388—21no—
453#384C22×C15111yescharacteristic, complemented
454#380C22×C15111yescharacteristic
455#380C22×C15111yescharacteristic
456#380C22×C15111yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C22×C15111yescharacteristic, complemented
460#340C22×C15111yescharacteristic, complemented
461#340C22×C15111yescharacteristic, complemented
462#340C22×C15111yescharacteristic, complemented
463#340C22×C15111yescharacteristic, complemented
464#336C22×C15111yescharacteristic, complemented
465#336C22×C15111yescharacteristic, complemented
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C15111yescharacteristic
477C22×D4C23×C15111yescharacteristic
478C22×D4C23×C15111yescharacteristic
479C23×C4C23×C15111yescharacteristic
480C23×C4C23×C15111yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C15111yescharacteristic
485C22×C8C23×C15111yescharacteristic
486C22×C8C23×C15111yescharacteristic
487C22×C8C23×C15111yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C15111yescharacteristic
502C2×C4⋊C4C23×C15111yescharacteristic
503C2×C4⋊C4C23×C15111yescharacteristic
504C2×C4⋊C4C23×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C4⋊C4C23×C15111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C15111yescharacteristic
520C2×C22⋊C4D4×C15111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C15111yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C15114yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C15111yescharacteristic
554C24C2×D4×C15111yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C15112yes—
582C2×D4#41×C15112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4C2×D4×C15111yescharacteristic
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4C2×D4×C15111yescharacteristic
602C22×C4C2×D4×C15111yescharacteristic
603C22×C4#41×C15112yes—
604C22×C4#41×C15112yes—
605C22×C4C24×C15111yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C15112yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C15112yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C15112yes—
687C23C22×D4×C15111yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4#123×C15112yes—
737C2×C4AGL(1,ℤ/8)×C15112yes—
738C2×C4C22×D4×C15111yescharacteristic
739C2×C4C2×#41×C15111yescharacteristic
740C2×C4C2×#41×C15111yescharacteristic
741C2×C4C2×#41×C15111yescharacteristic
742C2×C4H(5,𝔽2)×C15111yescharacteristic
743C2×C4H(5,𝔽2)×C15111yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C15111yescharacteristic
778C22D42×C15111yescharacteristic
779C22#546×C15111yescharacteristic
780C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
781C22#575×C15111yescharacteristic
782C22#576×C15111yescharacteristic
783C22#577×C15111yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4#525×C15111yescharacteristic
795C4#538×C15111yescharacteristic
796C4#546×C15111yescharacteristic
797C4#551×C15111yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2#2418×C15111yescharacteristic
803C2#3094×C15111yescharacteristic
804C2#3096×C15111yescharacteristic
805C2#3267×C15111yescharacteristic
806C2#3274×C15111yescharacteristic
807C2#3319×C15111yescharacteristic
808C2#3324×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2408×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#482×C151C2semidirect
2. C2×#418×C151C2semidirect
4. #2354×C151C2semidirect
5. #2093×C151C2semidirect
6. #2071×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1926×C151C2semidirect
10. #1926×C151C2semidirect
11. #1875×C151C2semidirect
12. #1870×C151C2semidirect
13. #1854×C151C2semidirect
14. #1809×C151C2semidirect
15. #1786×C151C2semidirect
23. C2×#117×C151C22semidirect
25. C2×#107×C151C22semidirect
26. C2×#107×C151C22semidirect
27. C2×#106×C151C22semidirect
28. C2×#106×C151C22semidirect
39. C2×C22⋊C8×C151C22semidirect
40. C2×C22⋊C8×C151C22semidirect
48. #384×C151C22semidirect
51. #380×C151C22semidirect
54. C4×C4⋊C4×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
131. #102×C151D4semidirect
404. #24890C151direct (N × H)
405. C151#24890direct (N × H)
406. C2×#482C2×C151semidirect
407. C2×#418C2×C151semidirect
409. #2354C2×C151semidirect
410. #2093C2×C151semidirect
411. #2071C2×C151semidirect
412. #2034C2×C151semidirect
413. #2033C2×C151semidirect
414. #1926C2×C151semidirect
415. #1926C2×C151semidirect
416. #1875C2×C151semidirect
417. #1870C2×C151semidirect
418. #1854C2×C151semidirect
419. #1809C2×C151semidirect
420. #1786C2×C151semidirect
428. C2×#117C22×C151semidirect
430. C2×#107C22×C151semidirect
431. C2×#107C22×C151semidirect
432. C2×#106C22×C151semidirect
433. C2×#106C22×C151semidirect
444. C2×C22⋊C8C22×C151semidirect
445. C2×C22⋊C8C22×C151semidirect
453. #384C22×C151semidirect
456. #380C22×C151semidirect
459. C4×C4⋊C4C22×C151semidirect
460. #340C22×C151semidirect
461. #340C22×C151semidirect
462. #340C22×C151semidirect
463. #340C22×C151semidirect
464. #336C22×C151semidirect
465. #336C22×C151semidirect
536. #102D4×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#482×C1512
C2×#418×C1512
#2408×C1512
#2354×C1512
#2093×C1512
#2071×C1512
#2034×C1512
#2033×C1512
#1926×C1512
#1875×C1512
#1870×C1512
#1854×C1512
#1809×C1512
#1786×C1512
#24890151